TITLE

Nonlinear elliptic equations with large supercritical exponents

AUTHOR(S)
Molle, Riccardo; Passaseo, Donato
PUB. DATE
June 2006
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2006, Vol. 26 Issue 2, p201
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The paper deals with the existence of positive solutions of the problem -? u=up in O, u=0 on ?O, where O is a bounded domain of $$\mathcal{R}^n$$ , n= 3, and p>2. We describe new concentration phenomena, which arise as p? +8 and can be exploited in order to construct, for p large enough, positive solutions that concentrate, as p? +8, near submanifolds of codimension 2. In this paper we consider, in particular, domains with axial symmetry and obtain positive solutions concentrating near (n-2)-dimensional spheres, which approach the boundary of O as p? +8. The existence and multiplicity results we state allow us to find positive solutions, for large p, also in domains which can be contractible and even arbitrarily close to starshaped domains (while no solution can exist if O is starshaped and $$p\ge {2n\over n-2}$$ , as a consequence of the Poho�aev's identity).
ACCESSION #
20378191

 

Related Articles

  • Reconstruction of 3D Human Facial Images Using Partial Differential Equations. Elyan, Eyad; Ugail, Hassan // Journal of Computers;Oct2007, Vol. 2 Issue 8, p1 

    One of the challenging problems in geometric modeling and computer graphics is the construction of realistic human facial geometry. Such geometry are essential for a wide range of applications, such as 3D face recognition, virtual reality applications, facial expression simulation and computer...

  • Submanifolds with pointwise planar normal sections in a sphere. Li, Shi-jie // Journal of Geometry;2001, Vol. 70 Issue 1/2, p101 

    In this article, we prove that a submanifold of S[sup m] has pointwise 2- or 3-planar normal sections via the second standard immersion of S[sup m] if and only if it is totally geodesic in S[sup m].

  • No symmetry advantage when object matching involves accidental viewpoints. Koning, Arno; Van Lier, Rob // Psychological Research;Jan2006, Vol. 70 Issue 1, p52 

    The presupposed advantage of symmetrical objects over asymmetrical objects was investigated in an object matching task, using accidental and non-accidental viewpoints. In addition, the accidental views could be symmetric or asymmetric. When two non-accidental views were presented, symmetrical...

  • Hamiltonian stability of Lagrangian tori in toric K�hler manifolds. Hajime Ono // Annals of Global Analysis & Geometry;Jun2007, Vol. 31 Issue 4, p329 

    Abstract��Let (M,J,?) be a compact toric Khler manifold of dimC M=n and L a regular orbit of the T n-action on M. In the present paper, we investigate Hamiltonian stability of L, which was introduced by Y.-G. Oh (Invent. Math. 101, 501�519 (1990); Math. Z. 212, 175�192)...

  • Decomposition and minimality of lagrangian submanifolds in nearly K�hler manifolds. Sch�fer, Lars; Smoczyk, Knut // Annals of Global Analysis & Geometry;Mar2010, Vol. 37 Issue 3, p221 

    We show that Lagrangian submanifolds in six-dimensional nearly K�hler (non-K�hler) manifolds and in twistor spaces Z4 n+2 over quaternionic K�hler manifolds Q4 n are minimal. Moreover, we prove that any Lagrangian submanifold L in a nearly K�hler manifold M splits into a...

  • Null 2-type submanifolds of the Euclidean space E5 with non-parallel mean curvature vector. Dursun, Ugur // Journal of Geometry;Apr2007, Vol. 86 Issue 1/2, p73 

    Let M be a 3-dimensional submanifold of the Euclidean space E5 such that M is not of 1-type. We show that if M is flat and of null 2-type with constant mean curvature and non-parallel mean curvature vector then the normal bundle is flat. We also prove that M is an open portion of a 3-dimensional...

  • Some slant submanifolds ofS-manifolds. Carriazo, Alfonso; Fernández, Luis M.; Hans-Uber, María Belén // Acta Mathematica Hungarica;Jun2005, Vol. 107 Issue 4, p267 

    We study some special types of slant submanifolds ofS-manifolds related to the second fundamental form of the immersion: totallyf-geodesic andf-umbilical, pseudo-umbilical and austere submanifolds. We also give several examples of such submanifolds.

  • The Stability and Load-Carrying Capacity of Cylindrical Shells with Axisymmetric Dents. Gavrilenko, G. D.; Matsner, V. I. // International Applied Mechanics;Jul2002, Vol. 38 Issue 7, p861 

    The classical method of stability analysis and the reduced-stiffness method are used to evaluate the critical loads and the lower bounds of sensitivity to imperfections in buckling of longitudinally loaded elastic cylindrical shells with local imperfections in the form of axisymmetric...

  • Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition. Han, Zhiqing // Acta Mathematica Sinica;2000, Vol. 16 Issue 2, p349 

    In this paper we prove a very general result concerning solvability of the resonant problem: Δu + λ[sub κ] u + g(x, u) = h (x); u = 0, x ∈ ∂ Ω, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics